Atomic systems in regular lattices are intriguing systems for implementing ideas in quantum simulation and information processing. Focusing on laser cooled ions forming Wigner crystals in Penning traps, we find a robust and simple approach to engineering non-trivial 2-body interactions sufficient for universal quantum computation. We then consider extensions of our approach to the fast generation of large cluster states, and a non-local architecture using an asymmetric entanglement generation procedure between a Penning trap system and well-established linear Paul trap designs.